A horizontal rope is tied to a 50 kg box on frictionless...

Key Concepts

Newton's First Law

This law states that an object will remain at rest or continue moving at a constant velocity unless acted upon by a net external force. It is critical in understanding scenarios where the box is at rest or moving at a steady speed, implying that the net force—and therefore the net tension or other forces—is zero.

Newton's Second Law

Newton's Second Law, expressed as F = ma, relates the net force acting on an object to its mass and the acceleration produced. This concept is essential for analyzing the situation when the box is accelerating, as it indicates that the overall tension in the rope must account for both the mass and the given acceleration.

Tension

Tension is the force transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In the context of the problem, understanding tension is crucial as it is the force applied to move or hold the box under different conditions of motion.

Frictionless Surface

A frictionless surface eliminates the resistive force of friction, ensuring that the only significant horizontal force acting on the box is the applied tension. This concept simplifies the application of Newton's laws, as it removes the need to consider opposing frictional forces in the calculations.

Transcript

00:01 In this question, we are told a horizontal rope is tied to a 50 kilogram box and the box is on frictionless ice.

00:11 And we're asked to calculate the tension in the rope in a variety of cases.

00:17 Now, before we start to calculate the tension, the force in the rope, what i would like to do is do a free body diagram of this object.

00:27 Now, since we're really only interested in the motion in the x direction, i'm going to leave off the forces in the y direction.

00:37 So let's think about the forces in the x direction here.

00:41 First of all, the ice is frictionless, so that means that there is no horizontal friction.

00:47 There is no friction force acting on this object.

00:50 And we know that there is a tension force pulling on the object horizontally.

00:57 So the tension force is actually the only force in the x direction that's acting on this box.

01:03 So any force that's acting on this object in the x direction is completely coming from that tension force.

01:10 All right.

01:12 So let's look at our different cases here.

01:15 So the first case is what is the tension force when the box is at rest? so at rest means that the velocity is zero, but it also means that the acceleration is zero, right? the velocity is zero and it's not changing.

01:30 So this will imply that the force is also zero, right? so you can think about it using newton's first law or second law.

01:42 When the acceleration is equal to zero, the force acting on the object must also be equal to zero.

01:49 Okay.

01:50 So what does that imply? it implies that the tension in the rope is also equal to zero.

01:56 Okay, there is no other force acting in the x direction.

02:00 So if the total force is zero, then the tension also has to be zero.

02:05 If there was friction force, then it would be possible, you know, that the friction force is there balancing out the tension force.

02:12 The tension force could be non -zero.

02:14 But in this case, since there is no friction force, if the total force is zero, then tension has to be zero as well.

02:21 Okay, second case, the box moves at a steady five meters per second...

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